On the website zotero.org you can create a user profile for free. This will give you access to online backup (up to 300 MB of storage) of your references, notes, and the files you import into Zotero.
After creating a profile, you must also log in to Zotero on you device (settings --> sync).
Note, that to avoid surpassing your free limit, you can consider not sharing full-text content to your online backup, so you only have backup of the references, but not the files.
Once you've created a profile, you can create groups on zotero.org, and then share references including your notes, tags and attached files between members of the group. After creating a group, you can invite other users through their Zotero-username or email.
You can drag-and-drop individual references or whole folders from your personal Zotero library to your group libraries.